Those two templates should not be related in the manner you describe. I just tested this in my own tenant by disabling the verification email template through the dashboard and then proceeding to request a password reset to my user; this resulted in me receiving the reset password email as expected.

Have in mind that although the dashboard user interface does not show a toggle for the reset password email template the template itself can still be disabled individually so you should review if you’re not in the situation described in this other post: